Problem: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 4x + 9$ and $ JT = 2x + 23$ Find $CT$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {4x + 9} = {2x + 23}$ Solve for $x$ $ 2x = 14$ $ x = 7$ Substitute $7$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 4({7}) + 9$ $ JT = 2({7}) + 23$ $ CJ = 28 + 9$ $ JT = 14 + 23$ $ CJ = 37$ $ JT = 37$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {37} + {37}$ $ CT = 74$